Homotopy classification of finite group actions on aspherical spaces

TL;DR

This paper introduces a homotopy classification method for finite group actions on aspherical spaces, providing a complete classification for free actions and insights into non-free actions through spectral sequences.

Contribution

It presents a novel approach for classifying finite group actions on aspherical spaces, including a complete classification for free actions and new relations involving group cohomology.

Findings

Complete homotopy classification of free actions

Relations between group cohomology and subgroup lattice

Spectral sequences used to analyze non-free actions

Abstract

The author proposes a method for investigating actions of finite groups on aspherical spaces. Complete homotopy classification of free actions of finite groups on aspherical spaces is obtained. Also there are some results about non-free actions. For example a relation between the cohomology of finite groups and the lattice structure of its subgroups is obtained by the proposed method. This relation is formulated in terms of spectral sequences.